## On the Hardness of Graph Isomorphism

### Cached

### Download Links

by
Jacobo Torán

Venue: | SIAM J. COMPUT |

Citations: | 33 - 1 self |

### BibTeX

@MISC{Torán_onthe,

author = {Jacobo Torán},

title = {On the Hardness of Graph Isomorphism},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

We show that the graph isomorphism problem is hard under DLOGTIME uniform AC0 many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space) for every logarithmic space modular class ModkL and for the class DET of problems NC¹ reducible to the determinant. These are the strongest known hardness results for the graph isomorphism problem and imply a randomized logarithmic space reduction from the perfect matching problem to graph isomorphism. We also investigate hardness results for the graph automorphism problem.